Explainable cable force grading early warning method based on abnormal probability and severity cooperation

Abstract

The application discloses an interpretable cable force grading early warning method based on abnormal probability and severity cooperation and relates to the technical field of bridge structure health monitoring. Structural parameters, vibration responses and environmental load data of a cable component are acquired, modal frequencies are extracted, and cable force state characteristics and observation reliability characteristics are constructed. A Bayesian neural network is used to obtain cable force prediction results, model uncertainty and observation uncertainty. A dynamic health interval that changes with working conditions is established based on historical data of a health stage, an abnormal occurrence probability, an expected overrun amount and a non-saturated abnormal severity are calculated, and a cable force state is mapped to four levels of normal, attention, early warning and severity in combination with a severity change trend. The level is corrected through continuous time confirmation, and early warning reasons are output by using characteristic contribution and counterfactual analysis. The method can improve the reliability and interpretability of cable force anomaly detection and grading early warning.

Description

Technical Field

[0001] This invention relates to the field of bridge structural health monitoring technology, specifically to an interpretable cable stress classification and early warning method based on the synergy of anomaly probability and severity. Background Technology

[0002] Cable-stayed structures are crucial load-bearing components in bridges and long-span spatial structures, and their stress state directly affects the structural stress and service safety. Existing monitoring methods typically compare real-time cable stress with design values, completed bridge values, historical averages, or preset ranges. However, cable stress fluctuates with normal operating conditions such as temperature and operational loads. Using fixed reference values ​​or thresholds can easily misjudge changes in normal operating conditions as abnormalities or mask true anomalies.

[0003] Some methods use probability distributions, prediction intervals, or anomaly scores to improve detection reliability. However, bounded indicators such as anomaly probability gradually approach their upper limits as the degree of anomaly increases, making it difficult to continue distinguishing the severity of anomalies. Furthermore, relying solely on a single anomaly indicator for classification makes it difficult to consider the probability of anomalies occurring, the degree to which they exceed healthy boundaries, and their development trends. Short-term data fluctuations may also cause frequent changes in warning levels.

[0004] Furthermore, when machine learning methods are used for force identification, some models only provide deterministic prediction results, making it difficult to distinguish between the uncertainty caused by insufficient model cognition and observation noise. After the warning level is formed, it is also difficult to explain the main influencing features and their direction of change, resulting in a lack of verifiability of the warning results.

[0005] Therefore, existing technologies mainly suffer from problems such as insufficient adaptability of health baselines to changes in operating conditions, insufficient ability to distinguish severe abnormal stages, insufficient stability of grading results, and insufficient interpretability of prediction and early warning results. Summary of the Invention

[0006] To address the shortcomings of existing technologies, such as insufficient adaptability of health baselines to changes in operating conditions, insufficient ability to distinguish severe abnormal stages, insufficient stability of grading results, and insufficient interpretability of prediction and early warning results, this invention proposes an interpretable cable force grading and early warning method based on the synergy of abnormal probability and severity. This method utilizes multi-source monitoring features to estimate cable force and its uncertainty, establishes an adaptive health baseline for operating conditions, calculates the probability of abnormal occurrence, the severity of exceeding limits, and their changing trends, maps early warning levels accordingly, and outputs the main influencing features and explanations of abnormal causes, thereby realizing abnormal cable force detection and grading early warning.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: An interpretable cable force classification and early warning method based on the synergy of anomaly probability and severity is applied to the condition monitoring of cable-stayed components in bridges or long-span spatial structures. The method includes: acquiring structural parameters, vibration response data, and environmental load data of the cable-stayed component to be monitored; extracting at least one order of modal frequencies; and constructing cable force state features and observation reliability features; inputting the cable force state features and observation reliability features into a Bayesian neural network to obtain the cable force prediction probability distribution, and distinguishing between model uncertainty and observation uncertainty; establishing a baseline relationship between environmental load and healthy cable force using historical monitoring data of the cable component's healthy stages, and constructing a dynamic health interval that changes with operating conditions; and based on the cable force prediction probability distribution and the dynamic health interval... The probability of anomalies is calculated, and the severity of unsaturated anomalies is determined based on the expected exceedances on the low and high sides. The severity of unsaturated anomalies is smoothed, and the trend of anomaly severity is calculated. Based on the probability of anomalies, the severity of unsaturated anomalies, and the trend of anomaly severity, the cable force status is directly mapped to four levels: normal, attention, warning, and severe. The warning level is corrected by continuous confirmation through a sliding time window. The contribution of each cable force status characteristic to the cable force prediction result is calculated, and the impact of each cable force status characteristic on the current warning level is determined through counterfactual analysis between the current abnormal state and the healthy reference state. The main influencing characteristics that lead to the current warning level and their direction of change are output.

[0008] Furthermore, the cable components include stay cables, suspension cables, main cables, tie cables, or prestressed cables; the vibration response data includes one or more of acceleration response, displacement response, or velocity response, and is acquired by an acceleration sensor, displacement sensor, laser vibration measurement equipment, or machine vision measurement equipment.

[0009] Furthermore, multiple measuring points or synchronous observation areas are set on the cable component. The first few modal frequencies are extracted from the vibration response data of each measuring point or synchronous observation area. The statistical mean of the same modal frequencies extracted from different measuring points or different synchronous observation areas is used as the modal frequency input of the corresponding order. The cable force state characteristics consist of the cable length, mass per unit length, elastic modulus, cable diameter, and modal frequencies after working condition correction. The observation reliability characteristics consist of one or more of the following: spectral signal-to-noise ratio, consistency of identification results, coefficient of variation of modal frequencies, proportion of effective data, and proportion of abnormal data.

[0010] Furthermore, based on the change in cable temperature relative to the reference temperature, the cable length is corrected by combining the cable linear expansion coefficient, and the elastic modulus is corrected by combining the elastic modulus temperature correction coefficient. The corrected cable length and elastic modulus are then used to construct the cable force state characteristics.

[0011] Furthermore, the Bayesian neural network includes a cable force mean prediction branch and an observation uncertainty assessment branch. The cable force mean prediction branch takes the cable force state features as input and outputs the cable force prediction mean. The observation uncertainty assessment branch takes the implicit features of the cable force mean prediction branch and the observation reliability features as input and outputs the variance corresponding to the observation uncertainty. The variance corresponding to the model uncertainty is obtained by sampling the Bayesian weight parameters multiple times, and the total variance of the cable force prediction is determined according to the variances corresponding to the two types of uncertainty, forming the cable force prediction probability distribution.

[0012] Furthermore, a healthy baseline model is established using environmental load data as the independent variable and the predicted mean of cable force in the healthy stage as the dependent variable. When the environmental load data includes at least cable temperature, the healthy cable force baseline is determined based on temperature deviation, the square term of temperature deviation, and the rate of temperature change. A dynamic healthy interval is formed by combining the degree of dispersion of cable force in the healthy state relative to the healthy cable force baseline.

[0013] Furthermore, the probability of anomaly occurrence is used to characterize the likelihood that the cable force prediction result is outside the dynamic health interval; the low-side expected overlimit and the high-side expected overlimit characterize the expected deviation of the cable force from the lower limit of the dynamic health interval and the upper limit of the dynamic health interval, respectively; the sum of the expected overlimits on both sides is normalized relative to the width of the dynamic health interval to obtain the severity of the unsaturated anomaly.

[0014] Furthermore, the severity of unsaturated anomalies within the preset sliding time window is smoothed by median, and the trend of anomaly severity is calculated. The threshold for judging the warning level is determined based on the statistical distribution of the probability of anomaly occurrence, the severity of unsaturated anomalies, and the trend of anomaly severity in the healthy phase, and is directly mapped according to the classification rules of normal, attention, warning, and severe. When multiple level judgment conditions are met at the same monitoring time, the highest level is taken as the initial warning level.

[0015] Furthermore, instead of constructing a comprehensive index by weighting and summing the probability of anomaly occurrence, the severity of unsaturated anomalies, and the trend of anomaly severity changes, the four levels are directly mapped based on whether each index meets the corresponding level conditions. Within the sliding confirmation window, the confirmation level increases when the number of monitoring times that reach the target level reaches the preset confirmation number.

[0016] Furthermore, the feature perturbation method is used to calculate the global contribution of each cable force state feature to the cable force prediction result. The main sources of uncertainty are determined based on the proportion of model uncertainty and observation uncertainty to the total uncertainty of cable force prediction. The health reference value of the cable force state feature to be explained is determined from the historical monitoring data of the healthy stage. The cable force state feature to be explained in the current abnormal sample is replaced with the corresponding health reference value to construct counterfactual input features. Based on the changes in cable force prediction results, probability of abnormal occurrence, severity of unsaturated abnormality or warning level before and after replacement, the main influencing features and their direction of change are determined.

[0017] Compared with the prior art, the present invention has the following beneficial effects: This invention utilizes historical monitoring data from the health phase to establish a baseline relationship between environmental load and healthy cable force, enabling the healthy cable force baseline and dynamic health range to be adjusted according to changes in normal engineering conditions, thereby reducing false alarms and missed alarms caused by fixed reference values ​​or fixed alarm limits.

[0018] Based on the probability of anomaly occurrence, this invention further calculates the expected over-limit on the low side and the expected over-limit on the high side, and constructs an unsaturated anomaly severity. Even when the probability of anomaly occurrence is close to the upper limit, it can still distinguish different severe anomaly states based on the degree to which the cable force exceeds the dynamic health range.

[0019] This invention integrates the probability of anomaly occurrence, the severity of unsaturated anomalies, and the trend of anomaly severity changes, directly mapping the cable force status to four levels: normal, attention, warning, and severe. It eliminates the need to construct a comprehensive index through weighted summation and uses a sliding time window for continuous confirmation, reducing frequent jumps in warning levels.

[0020] This invention obtains model uncertainty and observation uncertainty separately through Bayesian neural networks, and can distinguish different sources of uncertainty such as insufficient training sample coverage, insufficient model cognition and reduced observation reliability, thereby improving the credibility of cable force anomaly detection results.

[0021] This invention identifies the main cable force state characteristics that cause cable force anomalies and changes in early warning levels by using global feature contributions and local counterfactual contributions, and provides the direction of change of the corresponding characteristics, making the results of anomaly detection and graded early warning traceable, and providing a basis for on-site verification, inspection arrangements and maintenance decisions. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of the overall process of the method of the present invention; Figure 2 This is a schematic diagram illustrating the changes over time of the predicted mean of cable force, the temperature-adaptive health baseline, and the dynamic health interval in an embodiment of the present invention. Figure 3This is a comparison chart of the probability of anomalies between the static health baseline and the temperature-adaptive health baseline in this embodiment of the invention; Figure 4 This is a schematic diagram illustrating the changes in the severity of unsaturated anomalies and the four-level warning levels over time in an embodiment of the present invention. Figure 5 This is a schematic diagram illustrating the global importance of each cable force state characteristic to the cable force mean prediction result in an embodiment of the present invention; Figure 6 This is a partial counterfactual interpretation diagram of the moment when the fourth-level severe state monitoring is first reached in an embodiment of the present invention. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be described below with reference to the accompanying drawings. The following implementation details are all derived from the data acquisition, feature construction, probabilistic force identification, dynamic health baseline, dual abnormal indicators, four-level early warning, and interpretable output processes adopted in the technical solutions of the present invention.

[0024] Reference Figure 1 This embodiment provides an interpretable stress classification early warning method based on the synergy of anomaly probability and severity, which specifically includes the following steps.

[0025] Step 1: Data Acquisition.

[0026] The structural parameters, vibration response data, and environmental load data of the cable component to be tested are acquired. The structural parameters include at least cable length, mass per unit length, elastic modulus, and cable diameter; the vibration response data includes one or more of acceleration response, displacement response, or velocity response, and can be acquired by an accelerometer, displacement sensor, laser vibration measurement equipment, or machine vision measurement equipment; the environmental load data is used to characterize changes in the normal operating conditions of the cable component.

[0027] This embodiment uses laboratory steel strand as the research object. Machine vision is used to acquire the vibration response of the cable component and identify the first three modal frequencies, while an accelerometer is used for comparison. Temperature sensors are placed on the cable surface to simultaneously collect the cable temperature. The specific processing procedure of the machine vision uses existing technology and will not be elaborated here.

[0028] The rate of change of the temperature of the cable can be expressed as:

[0029] In the formula, t represents the current monitoring time. The current temperature of the cable body at the moment of monitoring. Interval with the current monitoring time The temperature of the cable at the previous monitoring time. This represents the time interval between adjacent monitoring moments.

[0030] To form cable force identification samples, finite element method is used to calculate different cable forces, temperatures and boundary constraints to obtain the structural parameters, modal frequencies, temperature parameters, vibration characteristic reliability characterization quantities and reference cable forces of the cable components. The samples are then segmented according to a set time window to form a cable force identification sample set.

[0031] Step 2, Feature Construction.

[0032] The acquired data undergoes time synchronization, outlier handling, operating condition correction, and normalization. The first few modal frequencies are extracted from vibration response data from multiple measuring points or synchronous observation areas. The statistical mean of the same-order modal frequencies extracted from different measuring points or observation areas is used as the input for the corresponding modal frequencies. The mean of the first modal frequencies can be expressed as:

[0033] In the formula, For the first The first measurement point or synchronous observation area extracted the first First-order modal frequency, This refers to the number of measuring points or synchronous observation areas.

[0034] No. The coefficient of variation of the first modal frequencies can be expressed as:

[0035] In the formula, Extracted from different measuring points or synchronous observation areas Standard deviation of first-order modal frequencies.

[0036] The reliability characteristics of observation include one or more of the following: spectral signal-to-noise ratio, consistency of identification results between different measurement points or synchronous observation areas, coefficient of variation of each modal frequency, proportion of effective data and proportion of abnormal data, which are used to characterize the credibility of the current vibration feature extraction results.

[0037] Among them, the spectrum signal-to-noise ratio is used to characterize the signal noise level of the current vibration response, the consistency of identification results is used to characterize the consistency of identification results at different measuring points or synchronous observation areas, the coefficient of variation of each modal frequency is used to characterize the dispersion of the corresponding modal frequency, and the proportion of effective data and the proportion of abnormal data are used to characterize the proportion of effective data and abnormal data in the current analysis time window, respectively.

[0038] In this embodiment, the vibration response sampling records and modal frequency identification results of each measuring point or synchronous observation area within the current analysis time window are used as the statistical objects. For the first... The median of the first modal frequencies is calculated from the valid identification results checked through data integrity, sensor range, spectral signal-to-noise ratio, and modal search band. When the first When the identification result of a single measuring point or synchronous observation area satisfies the following formula, the identification result is determined to be consistent with the identification results of other measuring points or synchronous observation areas:

[0039] Consistency of recognition results Represented as:

[0040] In the formula, The nth modal frequency is extracted from the i-th measuring point or synchronous observation area at monitoring time t; The modal order used is... This refers to the number of measuring points or synchronous observation areas. To indicate a valid identification result, the value is 1 if the identification result is valid, and 0 otherwise. The consistency determination flag is set to 1 if the recognition result meets the consistency determination condition, and 0 otherwise; the consistency threshold is... Determined based on the statistical quantiles of the relative deviations of the frequencies of the same modality during the healthy stage.

[0041] Let the number of data records that should be obtained within the current analysis time window according to the sampling frequency and the number of measurement points be... The actual number of data records received was The number of data records that passed the timestamp, integrity, range, saturation, non-numerical, and spectral quality checks was [number missing]. The proportion of valid data Represented as:

[0042] For the actual received data, the number of data records that failed the above quality checks will be recorded as follows: The proportion of abnormal data Represented as:

[0043] The unreceived data is composed of the proportion of valid data. The data is not included in the count of abnormal data records. Abnormal data includes non-numerical data, duplicate or out-of-order timestamps, data where the sensor is out of range or saturated, data where no effective modal peaks are formed in the spectrum, data where the identification frequency exceeds the preset physical search range, or data where the identification result exceeds the robust statistical range of the healthy phase and has not been verified by other synchronous measurement points. Modal frequency changes that occur synchronously at multiple measurement points and are mutually corroborated are retained as possible structural state changes and are not removed as data quality anomalies.

[0044] The cable stress state characteristics consist of the cable length, mass per unit length, elastic modulus, cable diameter, and modal frequencies after correction for the current working condition, and can be expressed as:

[0045] in, The cable length is corrected for the current working conditions. This is the elastic modulus corrected for the current operating conditions.

[0046] To account for the influence of temperature on structural parameters, the cable length and elastic modulus are corrected based on a reference temperature and the cable body temperature. The correction relationships are as follows:

[0047]

[0048] In the formula, Reference temperature The lower rope is long. Reference temperature The elastic modulus below, is the coefficient of linear expansion of the cable. This is the temperature correction factor for the elastic modulus.

[0049] Step 3, probabilistic cable force identification.

[0050] A two-branch Bayesian neural network is constructed to establish the mapping relationship between cable component structural parameters, modal frequencies, environmental conditions, vibration characteristic reliability, and cable force. The Bayesian neural network includes a cable force mean prediction branch and an observation uncertainty assessment branch. The cable force mean prediction branch takes cable force state characteristics as input and outputs the predicted cable force mean. The observation uncertainty assessment branch combines the implicit features extracted by the cable force mean prediction branch with the observation reliability features, outputting the variance corresponding to the observation uncertainty caused by measurement noise, frequency discrepancies, and data fluctuations.

[0051] In this embodiment, the mean prediction branch includes two hidden layers, each with 15 neurons, and the activation function is the ReLU function; the network weights and biases are represented by a Gaussian probability distribution.

[0052] The observation uncertainty assessment branch will evaluate the latent features of the last hidden layer output of the cable mean prediction branch. With observation reliability characteristics The data is spliced ​​together, passed through a fully connected layer and ReLU activation, and then the log-variance corresponding to the observation uncertainty is output. And the observation uncertainty variance is obtained through exponential transformation:

[0053]

[0054] In the formula, This represents the output mapping of the observation uncertainty assessment branch. This indicates the training sample number. The observation uncertainty assessment branch does not require pre-setting observation variance labels; its training uses a heteroscedastic Gaussian negative log-likelihood function, with the reference force of the training samples as the reference. , Cable Force Prediction Mean And the loss constructed from the variance of observation uncertainty:

[0055] The approximate posterior distribution of the Bayesian weights is determined through variational inference, and the total loss function of the model is expressed as:

[0056] In the formula, This represents the number of samples in the current training batch. As the weight of the regularization term, These are the weight parameters of the Bayesian neural network. The approximate posterior distribution of the Bayesian weights. The prior distribution of the Bayesian weights, This represents the Kullback-Leibler divergence. The posterior parameters of the Soleus mean prediction branch, the observation uncertainty assessment branch, and the Bayesian weights are jointly trained using the same batch of training samples and updated in the same backpropagation.

[0057] During the model prediction process, the weight parameters of the Bayesian neural network are adjusted. Second sampling, obtained The cable force prediction results are as follows. The mean of the cable force predictions is expressed as:

[0058] The variance corresponding to the model uncertainty is expressed as:

[0059] The variance corresponding to observation uncertainty is expressed as:

[0060] The total variance of the Solaris prediction is expressed as:

[0061] In the formula, For the first Cable force prediction results obtained under sub-Bayesian weight parameter sampling conditions; For the first The variance corresponding to the observation uncertainty output by the observation uncertainty assessment branch under the sub-Bayesian weighted parameter sampling condition; where... Let be the total variance of the cable force prediction at the current monitoring time, and the corresponding total standard deviation of the cable force prediction is . .

[0062] Among them, model uncertainty is used to characterize the uncertainty caused by insufficient coverage of training samples or insufficient understanding of model parameters, while observation uncertainty is used to characterize the uncertainty caused by measurement noise and reduced observation reliability. In this embodiment, the cable force prediction random variable at the current monitoring time is represented as having a mean of variance is It follows a normal distribution.

[0063] Step 4: Dynamic health baseline.

[0064] Data from historical monitoring data of cable-stayed structures, confirmed to be in a normal state, were selected as health samples. A health baseline model was established using environmental load data as the independent variable and the predicted mean cable force during the healthy phase as the dependent variable. The healthy cable force baseline at the current monitoring time can be expressed as:

[0065] In the formula, The baseline function is established based on historical monitoring data of the health stage, used to describe the deterministic variation law of the predicted mean of cable force in the health state under environmental load changes; This represents the current environmental load data. The specific form of the baseline function g(·) can be determined based on the composition of the environmental load variables and the distribution characteristics of the healthy samples.

[0066] When the environmental load data includes at least the cable temperature, this embodiment uses the temperature deviation, the squared term of the temperature deviation, and the rate of temperature change as input features of the baseline model, that is:

[0067] The corresponding baseline function expression is:

[0068] Therefore, the baseline for healthy slack at the current monitoring time is:

[0069]

[0070]

[0071] In the formula, , , , To utilize the baseline model parameters determined using historical monitoring data from the health phase, The temperature change rate of the cable body.

[0072] In this embodiment, continuous monitoring data for 20 days prior to the occurrence of progressive cable stress reduction is used as the candidate healthy phase. Data that confirms no human-induced stress reduction in the cable components, no abnormalities in the cable body, anchoring devices, and loading devices, and whose vibration response, temperature, and reference cable stress data pass integrity and validity checks, and whose modal frequency identification results pass the aforementioned valid identification and consistency checks, constitute the historical monitoring dataset for the healthy phase. .

[0073] For the Using a healthy sample, construct the independent variables for the baseline model:

[0074] The mean of the serotonin force during the healthy phase is predicted. As the dependent variable, the baseline model parameters are determined using the least squares method. :

[0075] In the formula, .

[0076] Discrete parameters of cable force in healthy state relative to the healthy cable force baseline The coefficient of variation (COP) is used to characterize the normal fluctuation of the predicted cable force under healthy conditions around the healthy cable force baseline. It can be determined based on the residual standard deviation of the predicted cable force under healthy conditions relative to the healthy cable force baseline. When there is a healthy reference cable force and healthy dispersion parameters for an alternative reference loading condition, the healthy relative dispersion coefficient can also be calculated first.

[0077] Then, determine the health dispersion parameters based on the current health reference strength:

[0078] In the formula, and These are the healthy reference cable force and the healthy discrete parameter under the alternative reference loading condition, respectively. The healthy discrete parameter is used to characterize the normal fluctuation of the cable force prediction result around the healthy cable force baseline under the healthy state, and its dimension is the same as that of the cable force. This is the health reference tension under the current loading condition.

[0079] This embodiment uses the health interval coefficient. This corresponds to the range of three discrete health parameters on each side of the healthy cable force baseline. The value is determined based on the three-standard-deviation criterion; when the health residuals approximately follow a normal distribution, the theoretical coverage of the constructed health interval is approximately 99.73%. In engineering applications, the health interval coefficients can be adjusted based on the empirical coverage of the health stage residuals, the allowable false alarm rate, and structural maintenance requirements. Perform calibration.

[0080] A dynamic health interval is constructed based on the healthy cable force baseline and the discrete parameters of the cable force in the healthy state relative to the healthy cable force baseline, with its lower limit... and upper limit They are respectively:

[0081]

[0082] In the formula, The discrete parameters of the cable force under healthy conditions relative to the baseline of healthy cable force are denoted as . This represents the coefficient for the health interval.

[0083] Step 5: Calculate the two abnormal indicators.

[0084] Based on the cable force prediction probability distribution obtained in step three and the dynamic health interval obtained in step four, calculate the probability of an anomaly where the cable force falls outside the dynamic health interval:

[0085] In the formula, F t P(·) represents the cable force prediction random variable at the current monitoring time; P(·) represents the cable force prediction random variable at the current monitoring time. Given the current predicted probability distribution, the probability of this event occurring is given. When the predicted probability distribution is normal, the probability of the anomaly occurring can be expressed as:

[0086] In the formula, This is the cumulative distribution function of the standard normal distribution. The probability of an anomaly occurring. The value of is between 0 and 1. The larger the value, the higher the probability that the predicted distribution of is outside the dynamic health range.

[0087] To maintain discriminative power during severe anomaly phases, the expected excess on the lower side (when the filament force is below the lower limit of the dynamic health interval) and the expected excess on the higher side (when the filament force is above the upper limit of the dynamic health interval) are further calculated:

[0088]

[0089] in, E[·] represents the positive part operator; E[·] represents the random variable for predicting the current force. The mathematical expectation calculated from the probability distribution.

[0090] When the probability distribution of the cable prediction is a normal distribution, let:

[0091] In the formula, and These represent the lower limit of the dynamic health range, respectively. and upper limit Relative to the average of cable force prediction Standard deviation predicted by slew rate The standardized values ​​of the lower and upper boundaries are obtained after standardization.

[0092] The lower-side expected excess and the higher-side expected excess are expressed as follows:

[0093]

[0094] In the formula, It is the probability density function of the standard normal distribution.

[0095] The sum of the low-side expected excess and the high-side expected excess is normalized relative to the width of the dynamic health interval to obtain the severity of the non-saturation anomaly:

[0096] The probability of an anomaly occurrence is used to characterize the likelihood of cable force deviating from the dynamic healthy range, while the severity of the unsaturated anomaly is used to characterize the degree to which the predicted cable force exceeds the dynamic healthy range. As the degree to which cable force deviates from the dynamic healthy range continues to increase, the severity of the unsaturated anomaly continues to increase with the increase of the expected excess amount.

[0097] Step six, Level four warning.

[0098] Severity of unsaturated anomalies within a preset sliding time window Median smoothing is performed to obtain the severity of smoothing anomalies, denoted as . And based on the current monitoring time t and The smoothed anomaly severity difference and trend calculation time interval are used to determine the trend of anomaly severity changes. It is represented as:

[0099] In the formula, Calculate time intervals for trends; Used to characterize the rate of change of the severity of smoothing anomalies over time.

[0100] Based on the probability of abnormal occurrence in the health stage Severity of unsaturation anomaly and the trend of abnormal severity The statistical distribution determines the judgment thresholds for each level, and directly maps the stress state to four levels: normal, attention, warning, and severe. This invention does not weight and synthesize various indicators into a comprehensive health indicator, but rather retains the physical meaning of each indicator and maps them according to the grading rules.

[0101] In this embodiment, the following example thresholds are used for the graded judgment: Level 1 is the normal state, and routine monitoring is maintained when the conditions of Level 2 or above are not met; Level 2 is the state of concern, when... ,or ,or At that time, encrypted monitoring is conducted and monitoring data is verified; Level 3 is an early warning state, when and , or in or In the case of At that time, cable tension retesting and special inspections were carried out; Level IV is a serious condition, when ,or and At that time, it was determined to be a serious condition.

[0102] The threshold values ​​mentioned above are example values ​​for this embodiment. In practical applications, they can be calibrated based on the quantiles of monitoring data during the health stage of the cable-stayed structure, the allowable cable force deviation, and structural operation and maintenance requirements. Each warning level is judged in the priority order of Level 4, Level 3, Level 2, and Level 1. When the judgment conditions for multiple levels are met simultaneously at the same monitoring time, the highest level is determined as the candidate warning level.

[0103] To reduce frequent jumps in warning levels caused by measurement noise or a single abnormal time window, candidate warning levels are continuously assessed. In this embodiment, the warning level is confirmed to have increased when at least two out of the most recent three consecutive time windows reach the corresponding candidate level.

[0104] Step seven, interpretable output.

[0105] A global interpretation of the Bayesian neural network is performed, and a feature perturbation method is used to determine the overall influence of each cable force state feature on the cable force prediction result. The global contribution of each cable force state characteristic can be expressed as:

[0106] In the formula, The root mean square error is given under the original test set conditions. For the disturbance The root mean square error after considering the characteristics of each cable force state.

[0107] This embodiment uses a perturbation method to evaluate the global contribution of each cable force state characteristic. While keeping other input features and the reference cable force constant in the independent test set, the [missing information - likely a specific parameter or parameter] is [missing information - likely a specific parameter or parameter]. Each cable force state feature is randomly rearranged among different test samples to disrupt the correspondence between the feature and the reference cable force, while maintaining its value range and marginal distribution. The perturbed test set is then re-input into the trained Bayesian neural network, and the perturbed root mean square error is calculated. .

[0108] The larger the value, the higher the value. The greater the influence of individual cable force state features on the global cable force prediction results, the more effective the method can be. To reduce the fluctuations in results caused by a single random permutation, a fixed random seed can be used for permutation, or the same feature can be permuted multiple times independently, and the average of the global contributions calculated multiple times can be used as the final global contribution.

[0109] Based on the correlation between observation reliability characteristics and observation uncertainty, the impact of each observation reliability characteristic on the reliability of cable force prediction is determined; the proportion of model uncertainty is also considered. and the proportion of observation uncertainty They are respectively:

[0110]

[0111] Based on the relationship between the two, we can determine whether the uncertainty in the current cable force prediction mainly stems from insufficient model knowledge or reduced observation reliability.

[0112] A local counterfactual interpretation is performed for individual abnormal monitoring moments. First, health reference values ​​for the cable force characteristics to be explained are determined from historical monitoring data of the healthy phase.

[0113] When determining the health reference value for the cable state characteristics to be explained, the historical monitoring dataset of the health stage is used. Healthy samples with environmental conditions similar to those at the current anomaly monitoring time are selected. For cable force state characteristics that vary with operating conditions, such as modal frequency, temperature-corrected cable length, and temperature-corrected elastic modulus, the current cable temperature and temperature change rate are used as the main matching conditions. When the historical monitoring data of the healthy phase includes operational load information, matching can also be performed in conjunction with operational load conditions, and the median of the corresponding cable force state characteristics in the matched healthy samples is used as the health reference value.

[0114] For structural parameters such as mass per unit length and cable diameter, which remain largely unchanged with environmental conditions during monitoring, measured or calibrated values ​​from the healthy phase are used as health reference values. When the number of matching healthy samples is insufficient, several healthy samples closest to the current conditions are selected based on the standardized distance of the environmental condition parameters, and the median of the corresponding characteristics is used as the health reference value.

[0115] Then, the unexplained force state features in the current abnormal sample are replaced with the health reference value to obtain the counterfactual input features. The local counterfactual contribution of each cable force state characteristic can be expressed as:

[0116] In the formula, The mapping function representing the mean of the output force prediction of the trained Bayesian neural network; Indicates the first The counterfactual set of cable state features is formed by replacing each unexplained cable state feature with its corresponding health reference value.

[0117] Based on the changes in the average predicted cable force, probability of anomaly occurrence, severity of unsaturated anomaly, or warning level before and after the replacement, determine the degree of influence and direction of change of each cable force state characteristic to be explained on the current anomaly state, and form an explanation result including the average predicted cable force, prediction interval, probability of anomaly occurrence, severity of unsaturated anomaly, trend of anomaly severity change, mapping level, level triggering conditions, and main influencing characteristics.

[0118] Experimental verification.

[0119] This embodiment uses laboratory steel strand as the research object. The effective length of the steel strand is 3m, the mass per unit length is 0.123kg / m, and the modulus of elasticity is 1.95×10⁻⁶. 5 MPa, diameter 5mm. The two ends of the steel strand are installed on the loading frame by clamps. The cable force is applied and adjusted by the loading device, and the reference cable force is obtained by the force sensor. Temperature sensors are arranged on the surface of the cable to collect the cable temperature synchronously. The first three modal frequencies are obtained by the vibration measurement device.

[0120] (1) Model Sample Construction. Model samples were constructed based on the structural parameters, loading range, parameter measurement error, boundary constraint changes, and temperature conditions of the laboratory cable components. The sample parameters and their value ranges are shown in Table 1. 10,000 sets of simulation substitute samples were formed according to the field format and time window organization of the measured data, of which 8,000 sets were used for model training, 1,000 sets were used for verification, and 1,000 sets were used for testing.

[0121] Table 1. Model Sample Parameters and Value Range

[0122] (2) Probabilistic cable force recognition results. A two-branch Bayesian neural network with two hidden layers and 15 neurons in each layer was used for training. The mean and prediction interval of cable force prediction were verified using experimental data. The root mean square error of cable force recognition was 18.5N, the relative root mean square error was 3.19%, and the average relative error was 2.60%; the 95% prediction interval coverage rate was 94.7%.

[0123] (3) Dynamic health baseline verification. A 60kg loading condition was used as the healthy loading condition, with the corresponding reference cable force being... N, take N is used as the healthy reference tension. The healthy reference tension and the health discrete parameters under the separate reference loading conditions are as follows: N and N, from which the relative dispersion coefficient of health is obtained:

[0124] According to current health references N, the health discrete parameter in this embodiment is determined as follows: N After rounding to two decimal places, we get N. In this embodiment, the health interval coefficient is taken. The corresponding dynamic health range is Continuous hourly monitoring data was collected for 60 days, with cable temperature varying from 5 to 45°C. Dynamic health baseline parameters were determined using health data from the first 20 days. A gradual reduction in cable force was implemented starting from day 24, reaching a maximum reduction of 58.9 N on day 44.

[0125] like Figure 2 As shown, the temperature-adaptive health baseline and dynamic health range change with normal temperature operating conditions; as Figure 3 As shown, when a fixed health baseline is used, the probability of abnormalities occurring in the healthy phase is... The proportion exceeding 0.70 was 0.174%. After adopting a dynamic health baseline, the probability of abnormalities occurring in the healthy stage was... The proportion exceeding 0.70 decreased to 0.

[0126] (4) Verification of abnormal dual indicators and mapping levels. Based on the N-health reference cable force, cable force reduction conditions of 1%, 3%, 5%, 8%, and 10% were set respectively, and the probability of abnormal occurrence under each condition was calculated. Severity of unsaturation anomaly The mapping levels and results are shown in Table 2. When the cable tension reduction ratio increases from 8% to 10%, The value increased from 0.9931 to 0.9990, a relatively small change. The increase from 0.30431 to 0.50257 still reflects the further development of the cable force anomaly.

[0127] Table 2 Abnormal Indicators and Warning Levels under Different Cable Force Reduction Conditions

[0128] (5) Continuous graded early warning results. For example... Figure 4 As shown, in the continuous monitoring of alternative data, a gradual reduction in cable force was set starting from day 24.

[0129] The method of this invention maps the cable stress status to a Level 3 warning on day 29 and adjusts it to a Level 4 severe state on day 33. The maximum severity of the unsaturated anomaly during the monitoring period is 0.794. Through continuous judgment, short-term data fluctuations did not cause frequent jumps in the warning level.

[0130] (6) Interpretation of early warning results. For example... Figure 5 As shown, the first modal frequency, temperature-corrected cable length, second modal frequency, mass per unit length, and third modal frequency are the main characteristics affecting the mean of cable force prediction; the frequency variation coefficient, vibration response consistency, and spectral signal-to-noise ratio mainly affect the output of observation uncertainty.

[0131] A local counterfactual analysis was performed on the monitoring moment when the level 4 severe condition was first reached, such as... Figure 6 As shown, the continuous decrease in the first and second modal frequencies is the main influencing factor for the decline in the predicted mean of cable force; the normal cable force changes caused by cable temperature have been explained by the dynamic health baseline. The decrease in cable force after deducting the influence of operating conditions, the high severity of unsaturated anomalies and their continued development jointly trigger the Level IV warning.

[0132] As demonstrated by the above verification, the present invention can output the cable force anomaly detection results and the corresponding mapping level, and can explain which indicators trigger the current level, which cable force state characteristics contribute significantly to the judgment of cable force anomaly, and the direction of action of each characteristic, thereby providing a traceable basis for cable force retesting, special inspection and maintenance.

[0133] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them; for those skilled in the art, any equivalent substitutions or adjustments made to the embodiments without departing from the technical solutions of the present invention should still be based on the technical content recorded in this application.

Claims

1. An interpretable cable force classification and early warning method based on the synergy of anomaly probability and severity, applicable to the safety status monitoring of cable components in bridges or long-span spatial structures, characterized in that... include: Obtain the structural parameters, vibration response data, and environmental load data of the cable component to be tested, extract at least one order modal frequency, and construct cable force state characteristics and observation reliability characteristics; The cable force state characteristics and observation reliability characteristics are input into a Bayesian neural network to obtain the cable force prediction probability distribution and to distinguish between model uncertainty and observation uncertainty. By utilizing historical monitoring data of the healthy stage of cable components, a baseline relationship between environmental load and healthy cable force is established, and a dynamic healthy range is constructed that varies with working conditions. The probability of anomaly occurrence is calculated based on the predicted probability distribution of the cable force and the dynamic health interval, and the severity of the non-saturation anomaly is determined based on the expected excess amount of the cable force when it is below the lower limit of the dynamic health interval and above the upper limit of the dynamic health interval. The severity of unsaturated anomalies is smoothed and the trend of anomaly severity is calculated. Based on the probability of anomaly occurrence, the severity of unsaturated anomalies, and the trend of anomaly severity, the cable force status is directly mapped to four levels: normal, attention, warning, and severe. The warning level is corrected by continuous confirmation through a sliding time window. Based on the cable force state characteristics, cable force prediction results, and warning levels of the Bayesian neural network, the contribution of each cable force state characteristic to the cable force prediction results is calculated, and a counterfactual analysis is performed between the current abnormal state and the healthy reference state. Based on the counterfactual analysis results, the influence of each cable force state characteristic on the current warning level is determined, and the main influencing characteristics that lead to the current warning level and their direction of change are output.

2. The interpretable stress classification early warning method based on the synergy of anomaly probability and severity as described in claim 1, characterized in that, The cable components include stay cables, suspension cables, main cables, tie cables, or prestressed cables; The vibration response data includes one or more of acceleration response, displacement response, or velocity response, and is acquired through an acceleration sensor, displacement sensor, laser vibration measurement equipment, or machine vision measurement equipment.

3. The interpretable stress classification early warning method based on the synergy of anomaly probability and severity as described in claim 1, characterized in that, Multiple measuring points or synchronous observation areas are set on the cable member. The first few modal frequencies are extracted from the vibration response data of each measuring point or synchronous observation area. The statistical mean of the same modal frequencies extracted from different measuring points or different synchronous observation areas is used as the modal frequency input of the corresponding order. The cable force state characteristics are composed of the cable length, mass per unit length, elastic modulus, cable diameter, and modal frequencies after working condition correction; The observation reliability characteristics consist of one or more of the following: spectral signal-to-noise ratio, consistency of identification results, coefficient of variation of frequency of each modality, proportion of valid data, and proportion of abnormal data.

4. The interpretable stress classification early warning method based on the synergy of anomaly probability and severity as described in claim 1, characterized in that, Based on the change in cable temperature relative to the reference temperature, the cable length is corrected by combining the cable linear expansion coefficient, and the elastic modulus is corrected by combining the elastic modulus temperature correction coefficient to obtain the cable length and elastic modulus under the current working condition. The corrected cable length and elastic modulus are then used to construct the cable force state characteristics.

5. The interpretable stress classification early warning method based on the synergy of anomaly probability and severity according to claim 1, characterized in that, The Bayesian neural network includes a branch for predicting the mean value of the stress and a branch for evaluating observation uncertainty. The cable force mean prediction branch takes the cable force state characteristics as input and outputs the cable force prediction mean; The observation uncertainty assessment branch takes the implicit features of the cable mean prediction branch and the observation reliability features as inputs, and outputs the variance corresponding to the observation uncertainty. The variance corresponding to the model uncertainty is obtained by sampling the Bayesian weight parameters multiple times. The total variance of the cable force prediction is determined based on the variance corresponding to the model uncertainty and the variance corresponding to the observation uncertainty, so as to form the cable force prediction probability distribution.

6. The interpretable stress classification early warning method based on the synergy of anomaly probability and severity according to claim 1, characterized in that, A healthy baseline model was established using environmental load data as the independent variable and the mean cable force prediction during the healthy phase as the dependent variable. When the environmental load data includes at least the cable temperature, the healthy cable force baseline is determined based on the temperature deviation, the square term of the temperature deviation, and the temperature change rate. The dynamic healthy range is then formed by combining the degree of dispersion of the cable force under the healthy state relative to the healthy cable force baseline.

7. The interpretable stress classification early warning method based on the synergy of anomaly probability and severity according to claim 1, characterized in that, The probability of an anomaly occurring is used to characterize the likelihood that the cable force prediction result is outside the dynamic health range. The expected over-limit includes the low-side expected over-limit when the cable force is lower than the lower limit of the dynamic health interval and the high-side expected over-limit when the cable force is higher than the upper limit of the dynamic health interval. The sum of the expected over-limit on the low side and the expected over-limit on the high side is normalized relative to the width of the dynamic health interval to obtain the severity of the unsaturated anomaly. The severity of the unsaturated anomaly continues to increase as the cable force deviates from the dynamic health interval.

8. The interpretable stress classification early warning method based on the synergy of anomaly probability and severity according to claim 1, characterized in that, The severity of unsaturated anomalies within a preset sliding time window is smoothed by median, and the judgment thresholds corresponding to each warning level are determined based on the statistical distribution of the probability of anomaly occurrence, severity of unsaturated anomalies, and the trend of anomaly severity changes during the healthy phase. When the probability of an anomaly, the severity of the unsaturated anomaly, and the trend of the anomaly severity are all below the threshold corresponding to the attention status, the state is determined to be normal. When any one of these indicators reaches the threshold corresponding to the attention status, the state is determined to be attention status. When the probability of an anomaly and the severity of the unsaturated anomaly both reach the threshold corresponding to the warning status, or when the probability of an anomaly or the severity of the unsaturated anomaly reaches the threshold corresponding to the attention status, the trend of the anomaly severity reaches the trend threshold corresponding to the warning status, the state is determined to be warning status. When the severity of the unsaturated anomaly reaches the severity threshold corresponding to the severe status, or when the probability of an anomaly reaches the probability threshold corresponding to the severe status and the severity of the unsaturated anomaly reaches the joint judgment threshold corresponding to the severe status, the state is determined to be severe status. When multiple level judgment conditions are met at the same monitoring time, the highest level is determined as the initial warning level.

9. The interpretable stress classification early warning method based on the synergy of anomaly probability and severity according to claim 8, characterized in that, The four levels are not constructed by weighting and summing the probability of anomaly occurrence, the severity of unsaturated anomalies, and the trend of anomaly severity changes to form a comprehensive index. Instead, they are directly mapped based on whether each index meets the conditions of the corresponding level. Within a sliding confirmation window that includes a preset number of monitoring times, when the number of monitoring times that reach the target level is not less than the preset number of confirmations, the final warning level will be raised to the target level.

10. The interpretable stress classification early warning method based on the synergy of anomaly probability and severity according to claim 1, characterized in that, The characteristic perturbation method is used to calculate the global contribution of each cable force state characteristic to the cable force prediction result. The main source of the current uncertainty is determined based on the proportion of model uncertainty and observation uncertainty to the total uncertainty of cable force prediction. Health reference values ​​for each unexplained cable force state feature are determined from historical monitoring data of the healthy phase. The unexplained cable force state features in the current abnormal sample are replaced with the corresponding health reference values ​​to construct counterfactual input features. Based on the changes in cable force prediction results, probability of abnormal occurrence, severity of unsaturated abnormality, or warning level before and after replacement, the main influencing features that lead to the current warning level and their direction of change are determined.

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